Axioms, Volume 14, Issue 1

Deep learning methods using neural networks for solving partial differential equations (PDEs) have emerged as a new paradigm. However, many of these methods approximate solutions by optimizing loss functions, often encountering convergence issues and...

In this paper, we use the averaging method to find an approximate solution for the optimal control of parabolic differential inclusion with fast-oscillating coefficients on a semi-axis.

This work aims to provide approximate solutions for singularly perturbed problems with periodic boundary conditions using quintic B-splines and collocation. The well-known Shishkin mesh strategy is applied for mesh construction. Convergence analysis...

This research presents a new form of iterative technique for Garcia-Falset mapping that outperforms previous iterative methods for contraction mappings. We illustrate this fact through comparison and present the findings graphically. The research als...

Additive manufacturing technologies have allowed the production of complex geometries that are typically obtained by applying topology optimization techniques. The outcome of the optimization process is a tessellated geometry, which has reduced aesth...

In this paper, we introduce a quantum private comparison (QPC) protocol designed for two players to securely and privately assess the equality of their private information. The protocol utilizes four-particle cluster states prepared by a semi-honest...

We examine the qualitative properties of ionic flows through membrane channels via Poisson–Nernst–Planck (PNP) type models with steric effects under relaxed electroneutrality boundary conditions, and more realistic setups in the study of...

A problem that geometers have always been concerned with is when a closed manifold is isometric to a round sphere. A classical result shows that a closed locally conformally flat Einstein manifold is always isometric to a quotient of a round sphere....

This paper considers the Horn’s hypergeometric function $H_3$, which is closely related to other hypergeometric functions and has various mathematical or physical applications. The problem of analytical extension of this function is solved using a...

We elaborate on the brane configuration that gives rise to a QCD-like gauge theory that confines at low energies and becomes scale invariant at the highest energies. In the limit where the rank of the gauge group is large, a gravitational description...

Orthogonal polynomials on radial rays in the complex plane were introduced and studied intensively in several papers almost three decades ago. This paper presents an account of such kinds of orthogonality in the complex plane, as well as a number of...

Outlier values and rankings are important for emphasizing data distribution variability, which improves the accuracy and effectiveness of variance estimations. To enhance the estimation of finite population variance in a two-phase sampling framework,...

Predators impact prey populations directly through consumption and indirectly via trait-mediated effects like predator-induced emigration (PIE), where prey alter movement due to predation risk. While PIE can significantly influence prey dynamics, its...

In this paper, we give examples that improve the lower bound on the maximum number of halving lines for sets in the plane with 35, 59, 95, and 97 points and, as a consequence, we improve the current best upper bound of the rectilinear crossing number...

In this paper, we study some homogeneity properties of a semi-direct extension of the Heisenberg group, known in literature as the hyperbolic oscillator (or Boidol) group, equipped with the left-invariant metrics corresponding to the ones of the osci...

This paper explores the implications of modifying the canonical Heisenberg commutation relations over two simple systems, such as the free particle and the tunnel effect generated by a step-like potential. The modified commutation relations include p...

The aim of this paper is to apply polynomial approximation by sums of squares in several real variables to the multidimensional moment problem. The general idea is to approximate any element of the positive cone of the involved function space with su...

In this paper, we consider the semilinear Dirichlet problem $\left({\mathcal{P}}_{\epsilon }\right):-\Delta u+V\left(x\right)u=u^{{\displaystyle \frac{n+2}{n-2}}-\epsilon }$, $u>0$ in $\Omega$, $u=0$ on ∂$\Omega$, where $\Omega$ is a bounded regular domain in ${\mathbb{R}}^n$, $n\ge 4$, $\epsilon$ is a small posit...

In this effort, we extend the fractal–fractional operators into the complex plane together with the quantum calculus derivative to obtain a quantum–fractal–fractional operators (QFFOs). Using this newly created operator, we create a...

A hypersurface $M^n$ in a real space form ${\mathbf{R}}^{n+1}$, $S^{n+1}$, or $H^{n+1}$ is isoparametric if it has constant principal curvatures. This paper is a survey of the fundamental work of Cartan and Münzner on the theory of isoparametric hypersurfaces in real space...

General asymptotic expansion of the $(p,k)$-gamma function is obtained and various approaches to this expansion are studied. The numerical precision of the derived asymptotic formulas is shown and compared. Results are applied to the analogues of digam...

When modeling real-world data, we face the challenge of determining which probability distribution best represents the data. To address this intricate problem, we rely on goodness-of-fit tests. However, when the data come from a bivariate negative bi...

In this paper, a fractional-order eco-epidemiological model with two disease strains in the predator population incorporating harvesting is formulated and analyzed. The model assumes that the population is divided into a prey population, a susceptibl...

Since the early 2000s, fuzzy mathematics has fostered a stream of research on the financial valuation of assets incorporating optionality. This paper makes two contributions to this field. First, it conducts a bibliographical analysis of contribution...

One of the most significant solution concepts in cooperative grey game theory is the grey Shapley value. This value is a fascinating one among the models and methods of operations research, and has been the subject of extensive study by other researc...

The Lucas balancing polynomial is linked to a family of bi-starlike functions denoted as ${\mathcal{S}}_{sc}^c(\vartheta ,\Xi \left(x\right))$, which we present and examine in this work. These functions are defined with respect to symmetric conjugate points. Coefficient estimate...

This paper is concerned with an equilibrium problem for an elastic structure consisting of a plate and an elastic beam connected to each other at a given point. We consider two cases: In the first one, the elastic beam is connected to a rigid part of...

For each n-dimensional real Banach space X, each positive integer m, and each bounded set $A\subseteq X$ with diameter greater than 0, let ${\beta }_X(A,m)$ be the infimum of $\delta \in (0,1]$ such that $A\subseteq X$ can be represented as the union of m subsets of...

In this paper, we prove existence and regularity results for a nonlinear elliptic problem of p-Laplacian type with a singular potential like ${\displaystyle \frac{f}{u^{\gamma }}}$ and a lower order term $bu$, where u is the solution and b and f are only assumed to be summable func...

The primary objective of this research is to investigate the notion of elliptic-valued metric spaces and prove new fixed-point theorems for diverse generalized contractions. Our contributions extend several existing results in the field. To underscor...

The overlap function has been extensively utilized across various fields. In this paper, we introduce the concepts of the similarity and $\delta$-equality of overlap functions to measure the degree of similarity between two overlap functions. Subseque...

This paper introduces a mathematical framework for defining and quantifying self-identity in artificial intelligence (AI) systems, addressing a critical gap in the theoretical foundations of artificial consciousness. While existing approaches to arti...

Let X be a centered random vector in a finite-dimensional real inner product space $\mathcal{E}$. For a subset C of the ambient vector space V of $\mathcal{E}$ and $x,y\in V$, write $x{⪯}_{C}y$ if $y-x\in C$. If C is a closed convex cone in $\mathcal{E}$, then ${⪯}_C$ is a preo...

This article primarily examines the approximation properties of a weighted Sobolev space $W_{2,\kappa }^r$ defined on a sphere ${\mathbb{S}}^{d-1}$ equipped with Gaussian measures. Specifically, this study focuses on both the average case and probabilistic case sett...

In this study, we introduce generalized k-order Fibonacci and Lucas (F&L) polynomials that allow the derivation of well-known polynomial and integer sequences such as the sequences of k-order Pell polynomials, k-order Jacobsthal polynomials and k...

This paper explores the application of automated reasoning tools, specifically those implemented in GeoGebra Discovery, to the perimeter-area inequality in triangles. Focusing on the computational complex and real algebraic geometry methods behind th...

Hyperuniform states of matter exhibit unusual suppression of density fluctuations at large scales, contrasting sharply with typical disordered configurations. Various types of hyperuniformity emerge in multicomponent disordered systems, significantly...

The zero-divisor graph of a commutative ring $\mathfrak{R}$ with a nonzero identity, denoted by $\Gamma \left(\mathfrak{R}\right)$, is an undirected graph where the vertex set $Z{\left(\mathfrak{R}\right)}^{*}$ consists of all nonzero zero-divisors of $\mathfrak{R}$. Two distinct vertices a and b in $\Gamma \left(\mathfrak{R}\right)$ are adjacent if a...

We study a bilinear optimal control problem for an evolution equation with a nonlinear term that depends on both the state and its time integral. First, we establish existence and uniqueness results for this evolution equation. Then, we derive weak m...

This study addresses the fuzzy parameters (coefficient) determination for the logistic population growth model, proposing a novel methodology based on fuzzy logic concepts. Population dynamics are often modeled using differential equations whose para...

We start with the 50-component relativistic matrix equation for a hypothetical spin-2 particle in the presence of external electromagnetic fields. This equation is hypothesized to describe a particle with an anomalous magnetic moment. The complete wa...

In this paper, the asymptotic behavior of the modified Mellin transform ${\mathcal{Z}}_2\left(s\right)$, $s=\sigma +it$, of the fourth power of the Riemann zeta function is characterized by weak convergence of probability measures in the space of analytic functions. The main re...

In this work, the fractal continuum Maxwell law for the creep phenomenon is introduced. By mapping standard integer space-time into fractal continuum space-time using the well-known Balankin’s approach to variable-order fractal calculus, the fr...

This study introduces a novel approach to accelerated life test experiments by examining competing risk factors using the Tampered Random Variable (TRV) model. This approach remains extensively unexplored in current research. The methodology is imple...

Hybrid sets are defined as multisets having also negative multiplicities, i.e. as functions from a crisp set to the group of all integers. In this article, we introduce a significant advancement in hybrid sets through the concept of group-valued mult...

Finding analytical closed-form solutions for the sums of powers of the first n positive integers is a classical problem of number theory. Analytical methods of constructing such sums produce complicated formulae of polynomials of a higher order, but...

The classical problem of stabilization of the controlled inverted pendulum is considered in the case of stochastic perturbations of the type of Poisson’s jumps. It is supposed that stabilized control depends on the entire trajectory of the pend...

We study the geometric properties of some classes of mappings for which an inverse Poletsky modular inequality holds. In these classes of mappings, we give some extensions of the theorems of Lindelőf and Fatou from the classical complex analysis...

In certain stages of the application of a type-2 fuzzy logic system, it is necessary to perform operations between input or output fuzzy variables in order to compute the union, intersection, aggregation, complement, and so forth. In this context, op...

We explore the existence and uniqueness of solutions to nonlinear fractional differential equations (FDEs), defined in the sense of RL-fractional derivatives of order $\eta \in (1,2)$. The nonlinear term is assumed to have a discontinuity at zero. By...